Preface to The Primitives of Vector Calculus Robert R. Curtis, San Joaquin Delta College

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It is a little known fact that the early cavepeople of the paleolethargic era were profoundly interested in vector calculus.

Some years ago archaeologists discovered drawings on cave walls in southern France which date back some 50,000 years. The drawings depicted arrows being projected at bison­type animals.

The true nature of these drawings was a closely guarded secret by the archaeological community for many years. Thanks to the academic popparrazzi, it has recently been uncovered that these images of the bison­type animals were added many thousands of years later, placed on top of the original drawings of the arrows   ­   apparently the work of a neanderthal graffiti artist.

The original drawings of sets of arrows   ­   today referred to as "vectors"   ­   point to the early hominid's deep interest in the calculus of vectors.

Furthermore, many stone objects have been found at cave dwelling sites. Misinterpreted by archaeologists as being "wheels", "plates", and "cups", it is now believed that these were three-dimensional objects forged by stone and chisel as part of their visualization of the geometry of three­space. "Plates" apparently were investigations involving polar coordinates, "wheels" part of the study of 3D volume problems, and "cups" were actually early attempts at understanding the circular paraboloid

How much did the early cavepeople understand about vector calculus? Did they know about cross­products for creating a new vector perpendicular to two given vectors? Did they understand how to differentiate a vector field? Did they truly understand the Fundamental Theorem of Calculus in n-dimensions? We may never know the true extent of their knowledge of vector calculus.

Our goal in this text will be to bring the cavepeople of the paleolethargic (and any of their modern­day brethren) towards a modern, visually-based understanding of vector calculus by utilizing the most modern of tools and topics. Some prehistoric tools will still be used, including pencils, chalk, and algebra. But the majority of our exposition will be for the 21st-century relative of the cavedweller: the impatient multimedia digital warrior.

Those readers wishing to learn vector calculus from a purely prehistoric approach should have no problem finding another book that attempts to investigate this subject from an algebraic point of view. You might even be able to get a good deal on some carving stone to help with your visualization, should you need any.